Prices start at $135,700 for the Model S P100D and $136,700 for the Model X P100D. Prices include a $1,200 destination charge.

The vehicles can be ordered immediately at Tesla stores, with deliveries slated to begin next month.

Tesla says the new 2016 Tesla Model S P100D with Ludicrous mode is the world's quickest production car.

The twin-motor Model S P100D, with upgraded 100-kilowatt-hour battery pack and Ludicrous mode upgrade, is capable of accelerating from zero to 60 mph in 2.5 seconds, according to Tesla.

Its crossover companion, the Tesla Model X P100D, is able to do the same sprint in 2.9 seconds, Tesla estimates, making it the world's quickest utility vehicle.

Moreover, range between charges climbs to 315 miles on the Model S P100D, giving it the longest range of any production electric vehicle in the world. Range is 289 miles on the Model X P100D.

"Range anxiety has long been one of the biggest obstacles for the adoption of electric cars," said Jessica Caldwell, Edmunds.com executive director of industry analysis. "By developing vehicles with longer-range batteries, Tesla is moving the ball forward not just for itself but the entire EV industry.

"For now, only folks who can afford a six-figure vehicle will be able to enjoy the luxury of faster speeds and longer range, but this is the sort of innovation that will improve the electric car's reputation with skeptical shoppers. Now the challenge is to make this sort of technology available at lower price points."

Tesla customers who have ordered but not yet taken delivery of a P90D Ludicrous Model S or Model X can upgrade to the 100-kWh battery pack for $10,000. Existing P90D owners can upgrade for $20,000, which includes the cost of recycling the old 90-kWh pack.